In this work, we add some more facts on fan-crossing free graphs,
which demonstrate the power of these graphs. Some of the results come
as expected, for example the NP-hardness, which is stated as an open problem in
[1]}. As our main contribution, we study
three graph operations, which are used to distinguish fan-crossing
free graphs from other well-known classes of beyond-planar graphs
including fan-crossing graphs.
In particular, we prove the following:
